# 5. Kaleidoscope: Extending the Language: Control Flow

- Chapter 5 Introduction
- If/Then/Else
  - Lexer Extensions for If/Then/Else
  - AST Extensions for If/Then/Else
  - Parser Extensions for If/Then/Else
  - LLVM IR for If/Then/Else
  - Code Generation for If/Then/Else
- ‘for’ Loop Expression
  - Lexer Extensions for the ‘for’ Loop
  - AST Extensions for the ‘for’ Loop
  - Parser Extensions for the ‘for’ Loop
  - LLVM IR for the ‘for’ Loop
  - Code Generation for the ‘for’ Loop
- Full Code Listing

## 5.1. Chapter 5 Introduction

Welcome to Chapter 5 of the “Implementing a language with LLVM” tutorial. Parts 1-4 described the implementation of the simple Kaleidoscope language and included support for generating LLVM IR, followed by optimizations and a JIT compiler. Unfortunately, as presented, Kaleidoscope is mostly useless: it has no control flow other than call and return. This means that you can’t have conditional branches in the code, significantly limiting its power. In this episode of “build that compiler”, we’ll extend Kaleidoscope to have an if/then/else expression plus a simple ‘for’ loop.

## 5.2. If/Then/Else

Extending Kaleidoscope to support if/then/else is quite straightforward. It basically requires adding lexer support for this “new” concept to the lexer, parser, AST, and LLVM code emitter. This example is nice, because it shows how easy it is to “grow” a language over time, incrementally extending it as new ideas are discovered.

Before we get going on “how” we add this extension, lets talk about “what” we want. The basic idea is that we want to be able to write this sort of thing:

    def fib(x)
      if x < 3 then
        1
      else
        fib(x-1)+fib(x-2);

In Kaleidoscope, every construct is an expression: there are no statements. As such, the if/then/else expression needs to return a value like any other. Since we’re using a mostly functional form, we’ll have it evaluate its conditional, then return the ‘then’ or ‘else’ value based on how the condition was resolved. This is very similar to the C ”?:” expression.

The semantics of the if/then/else expression is that it evaluates the condition to a boolean equality value: 0.0 is considered to be false and everything else is considered to be true. If the condition is true, the first subexpression is evaluated and returned, if the condition is false, the second subexpression is evaluated and returned. Since Kaleidoscope allows side-effects, this behavior is important to nail down.

Now that we know what we “want”, lets break this down into its constituent pieces.

### 5.2.1. Lexer Extensions for If/Then/Else

The lexer extensions are straightforward. First we add new variants for the relevant tokens:

    (* control *)
    | If | Then | Else | For | In

Once we have that, we recognize the new keywords in the lexer. This is pretty simple stuff:

    ...
    match Buffer.contents buffer with
    | "def" -> [< 'Token.Def; stream >]
    | "extern" -> [< 'Token.Extern; stream >]
    | "if" -> [< 'Token.If; stream >]
    | "then" -> [< 'Token.Then; stream >]
    | "else" -> [< 'Token.Else; stream >]
    | "for" -> [< 'Token.For; stream >]
    | "in" -> [< 'Token.In; stream >]
    | id -> [< 'Token.Ident id; stream >]

### 5.2.2. AST Extensions for If/Then/Else

To represent the new expression we add a new AST variant for it:

    type expr =
      ...
      (* variant for if/then/else. *)
      | If of expr * expr * expr

The AST variant just has pointers to the various subexpressions.

### 5.2.3. Parser Extensions for If/Then/Else

Now that we have the relevant tokens coming from the lexer and we have the AST node to build, our parsing logic is relatively straightforward. Next we add a new case for parsing a if-expression as a primary expression:

    let rec parse_primary = parser
      ...
      (* ifexpr ::= 'if' expr 'then' expr 'else' expr *)
      | [< 'Token.If; c=parse_expr;
           'Token.Then ?? "expected 'then'"; t=parse_expr;
           'Token.Else ?? "expected 'else'"; e=parse_expr >] ->
          Ast.If (c, t, e)

### 5.2.4. LLVM IR for If/Then/Else

Now that we have it parsing and building the AST, the final piece is adding LLVM code generation support. This is the most interesting part of the if/then/else example, because this is where it starts to introduce new concepts. All of the code above has been thoroughly described in previous chapters.

To motivate the code we want to produce, lets take a look at a simple example. Consider:

    extern foo();
    extern bar();
    def baz(x) if x then foo() else bar();

If you disable optimizations, the code you’ll (soon) get from Kaleidoscope looks like this:

    declare double @foo()

    declare double @bar()

    define double @baz(double %x) {
    entry:
      %ifcond = fcmp one double %x, 0.000000e+00
      br i1 %ifcond, label %then, label %else

    then:    ; preds = %entry
      %calltmp = call double @foo()
      br label %ifcont

    else:    ; preds = %entry
      %calltmp1 = call double @bar()
      br label %ifcont

    ifcont:    ; preds = %else, %then
      %iftmp = phi double [ %calltmp, %then ], [ %calltmp1, %else ]
      ret double %iftmp
    }

To visualize the control flow graph, you can use a nifty feature of the LLVM ‘opt‘ tool. If you put this LLVM IR into “t.ll” and run “`llvm-as < t.ll | opt -analyze -view-cfg`”, a window will pop up and you’ll see this graph:

Example CFG

Another way to get this is to call “`Llvm_analysis.view_function_cfg f`” or “`Llvm_analysis.view_function_cfg_only f`” (where `f` is a “`Function`”) either by inserting actual calls into the code and recompiling or by calling these in the debugger. LLVM has many nice features for visualizing various graphs.

Getting back to the generated code, it is fairly simple: the entry block evaluates the conditional expression (“x” in our case here) and compares the result to 0.0 with the “`fcmp one`” instruction (‘one’ is “Ordered and Not Equal”). Based on the result of this expression, the code jumps to either the “then” or “else” blocks, which contain the expressions for the true/false cases.

Once the then/else blocks are finished executing, they both branch back to the ‘ifcont’ block to execute the code that happens after the if/then/else. In this case the only thing left to do is to return to the caller of the function. The question then becomes: how does the code know which expression to return?

The answer to this question involves an important SSA operation: the Phi operation. If you’re not familiar with SSA, the wikipedia article is a good introduction and there are various other introductions to it available on your favorite search engine. The short version is that “execution” of the Phi operation requires “remembering” which block control came from. The Phi operation takes on the value corresponding to the input control block. In this case, if control comes in from the “then” block, it gets the value of “calltmp”. If control comes from the “else” block, it gets the value of “calltmp1”.

At this point, you are probably starting to think “Oh no! This means my simple and elegant front-end will have to start generating SSA form in order to use LLVM!”. Fortunately, this is not the case, and we strongly advise not implementing an SSA construction algorithm in your front-end unless there is an amazingly good reason to do so. In practice, there are two sorts of values that float around in code written for your average imperative programming language that might need Phi nodes:

1. Code that involves user variables: `x = 1; x = x + 1;`
2. Values that are implicit in the structure of your AST, such as the Phi node in this case.

In Chapter 7 of this tutorial (“mutable variables”), we’ll talk about #1 in depth. For now, just believe me that you don’t need SSA construction to handle this case. For #2, you have the choice of using the techniques that we will describe for #1, or you can insert Phi nodes directly, if convenient. In this case, it is really really easy to generate the Phi node, so we choose to do it directly.

Okay, enough of the motivation and overview, lets generate code!

### 5.2.5. Code Generation for If/Then/Else

In order to generate code for this, we implement the `Codegen` method for `IfExprAST`:

    let rec codegen_expr = function
      ...
      | Ast.If (cond, then_, else_) ->
          let cond = codegen_expr cond in

          (* Convert condition to a bool by comparing equal to 0.0 *)
          let zero = const_float double_type 0.0 in
          let cond_val = build_fcmp Fcmp.One cond zero "ifcond" builder in

This code is straightforward and similar to what we saw before. We emit the expression for the condition, then compare that value to zero to get a truth value as a 1-bit (bool) value.

    (* Grab the first block so that we might later add the conditional branch
     * to it at the end of the function. *)
    let start_bb = insertion_block builder in
    let the_function = block_parent start_bb in

    let then_bb = append_block context "then" the_function in
    position_at_end then_bb builder;

As opposed to the C++ tutorial, we have to build our basic blocks bottom up since we can’t have dangling BasicBlocks. We start off by saving a pointer to the first block (which might not be the entry block), which we’ll need to build a conditional branch later. We do this by asking the `builder` for the current BasicBlock. The fourth line gets the current Function object that is being built. It gets this by the `start_bb` for its “parent” (the function it is currently embedded into).

Once it has that, it creates one block. It is automatically appended into the function’s list of blocks.

    (* Emit 'then' value. *)
    position_at_end then_bb builder;
    let then_val = codegen_expr then_ in

    (* Codegen of 'then' can change the current block, update then_bb for the
     * phi. We create a new name because one is used for the phi node, and the
     * other is used for the conditional branch. *)
    let new_then_bb = insertion_block builder in

We move the builder to start inserting into the “then” block. Strictly speaking, this call moves the insertion point to be at the end of the specified block. However, since the “then” block is empty, it also starts out by inserting at the beginning of the block. :)

Once the insertion point is set, we recursively codegen the “then” expression from the AST.

The final line here is quite subtle, but is very important. The basic issue is that when we create the Phi node in the merge block, we need to set up the block/value pairs that indicate how the Phi will work. Importantly, the Phi node expects to have an entry for each predecessor of the block in the CFG. Why then, are we getting the current block when we just set it to ThenBB 5 lines above? The problem is that the “Then” expression may actually itself change the block that the Builder is emitting into if, for example, it contains a nested “if/then/else” expression. Because calling Codegen recursively could arbitrarily change the notion of the current block, we are required to get an up-to-date value for code that will set up the Phi node.

    (* Emit 'else' value. *)
    let else_bb = append_block context "else" the_function in
    position_at_end else_bb builder;
    let else_val = codegen_expr else_ in

    (* Codegen of 'else' can change the current block, update else_bb for the
     * phi. *)
    let new_else_bb = insertion_block builder in

Code generation for the ‘else’ block is basically identical to codegen for the ‘then’ block.

    (* Emit merge block. *)
    let merge_bb = append_block context "ifcont" the_function in
    position_at_end merge_bb builder;
    let incoming = [(then_val, new_then_bb); (else_val, new_else_bb)] in
    let phi = build_phi incoming "iftmp" builder in

The first two lines here are now familiar: the first adds the “merge” block to the Function object. The second changes the insertion point so that newly created code will go into the “merge” block. Once that is done, we need to create the PHI node and set up the block/value pairs for the PHI.

    (* Return to the start block to add the conditional branch. *)
    position_at_end start_bb builder;
    ignore (build_cond_br cond_val then_bb else_bb builder);

Once the blocks are created, we can emit the conditional branch that chooses between them. Note that creating new blocks does not implicitly affect the IRBuilder, so it is still inserting into the block that the condition went into. This is why we needed to save the “start” block.

    (* Set a unconditional branch at the end of the 'then' block and the
     * 'else' block to the 'merge' block. *)
    position_at_end new_then_bb builder; ignore (build_br merge_bb builder);
    position_at_end new_else_bb builder; ignore (build_br merge_bb builder);

    (* Finally, set the builder to the end of the merge block. *)
    position_at_end merge_bb builder;

    phi

To finish off the blocks, we create an unconditional branch to the merge block. One interesting (and very important) aspect of the LLVM IR is that it requires all basic blocks to be “terminated” with a control flow instruction such as return or branch. This means that all control flow, including fall throughs must be made explicit in the LLVM IR. If you violate this rule, the verifier will emit an error.

Finally, the CodeGen function returns the phi node as the value computed by the if/then/else expression. In our example above, this returned value will feed into the code for the top-level function, which will create the return instruction.

Overall, we now have the ability to execute conditional code in Kaleidoscope. With this extension, Kaleidoscope is a fairly complete language that can calculate a wide variety of numeric functions. Next up we’ll add another useful expression that is familiar from non-functional languages...

## 5.3. ‘for’ Loop Expression

Now that we know how to add basic control flow constructs to the language, we have the tools to add more powerful things. Lets add something more aggressive, a ‘for’ expression:

    extern putchard(char);
    def printstar(n)
      for i = 1, i < n, 1.0 in
        putchard(42);  # ascii 42 = '*'

    # print 100 '*' characters
    printstar(100);

This expression defines a new variable (“i” in this case) which iterates from a starting value, while the condition (“i < n” in this case) is true, incrementing by an optional step value (“1.0” in this case). If the step value is omitted, it defaults to 1.0. While the loop is true, it executes its body expression. Because we don’t have anything better to return, we’ll just define the loop as always returning 0.0. In the future when we have mutable variables, it will get more useful.

As before, lets talk about the changes that we need to Kaleidoscope to support this.

### 5.3.1. Lexer Extensions for the ‘for’ Loop

The lexer extensions are the same sort of thing as for if/then/else:

    ... in Token.token ...
    (* control *)
    | If | Then | Else
    | For | In

    ... in Lexer.lex_ident...
        match Buffer.contents buffer with
        | "def" -> [< 'Token.Def; stream >]
        | "extern" -> [< 'Token.Extern; stream >]
        | "if" -> [< 'Token.If; stream >]
        | "then" -> [< 'Token.Then; stream >]
        | "else" -> [< 'Token.Else; stream >]
        | "for" -> [< 'Token.For; stream >]
        | "in" -> [< 'Token.In; stream >]
        | id -> [< 'Token.Ident id; stream >]

### 5.3.2. AST Extensions for the ‘for’ Loop

The AST variant is just as simple. It basically boils down to capturing the variable name and the constituent expressions in the node.

    type expr =
      ...
      (* variant for for/in. *)
      | For of string * expr * expr * expr option * expr

### 5.3.3. Parser Extensions for the ‘for’ Loop

The parser code is also fairly standard. The only interesting thing here is handling of the optional step value. The parser code handles it by checking to see if the second comma is present. If not, it sets the step value to null in the AST node:

    let rec parse_primary = parser
      ...
      (* forexpr
            ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression *)
      | [< 'Token.For;
           'Token.Ident id ?? "expected identifier after for";
           'Token.Kwd '=' ?? "expected '=' after for";
           stream >] ->
          begin parser
            | [<
                 start=parse_expr;
                 'Token.Kwd ',' ?? "expected ',' after for";
                 end_=parse_expr;
                 stream >] ->
                let step =
                  begin parser
                  | [< 'Token.Kwd ','; step=parse_expr >] -> Some step
                  | [< >] -> None
                  end stream
                in
                begin parser
                | [< 'Token.In; body=parse_expr >] ->
                    Ast.For (id, start, end_, step, body)
                | [< >] ->
                    raise (Stream.Error "expected 'in' after for")
                end stream
            | [< >] ->
                raise (Stream.Error "expected '=' after for")
          end stream

### 5.3.4. LLVM IR for the ‘for’ Loop

Now we get to the good part: the LLVM IR we want to generate for this thing. With the simple example above, we get this LLVM IR (note that this dump is generated with optimizations disabled for clarity):

    declare double @putchard(double)

    define double @printstar(double %n) {
    entry:
            ; initial value = 1.0 (inlined into phi)
      br label %loop

    loop:    ; preds = %loop, %entry
      %i = phi double [ 1.000000e+00, %entry ], [ %nextvar, %loop ]
            ; body
      %calltmp = call double @putchard(double 4.200000e+01)
            ; increment
      %nextvar = fadd double %i, 1.000000e+00

            ; termination test
      %cmptmp = fcmp ult double %i, %n
      %booltmp = uitofp i1 %cmptmp to double
      %loopcond = fcmp one double %booltmp, 0.000000e+00
      br i1 %loopcond, label %loop, label %afterloop

    afterloop:    ; preds = %loop
            ; loop always returns 0.0
      ret double 0.000000e+00
    }

This loop contains all the same constructs we saw before: a phi node, several expressions, and some basic blocks. Lets see how this fits together.

### 5.3.5. Code Generation for the ‘for’ Loop

The first part of Codegen is very simple: we just output the start expression for the loop value:

    let rec codegen_expr = function
      ...
      | Ast.For (var_name, start, end_, step, body) ->
          (* Emit the start code first, without 'variable' in scope. *)
          let start_val = codegen_expr start in

With this out of the way, the next step is to set up the LLVM basic block for the start of the loop body. In the case above, the whole loop body is one block, but remember that the body code itself could consist of multiple blocks (e.g. if it contains an if/then/else or a for/in expression).

    (* Make the new basic block for the loop header, inserting after current
     * block. *)
    let preheader_bb = insertion_block builder in
    let the_function = block_parent preheader_bb in
    let loop_bb = append_block context "loop" the_function in

    (* Insert an explicit fall through from the current block to the
     * loop_bb. *)
    ignore (build_br loop_bb builder);

This code is similar to what we saw for if/then/else. Because we will need it to create the Phi node, we remember the block that falls through into the loop. Once we have that, we create the actual block that starts the loop and create an unconditional branch for the fall-through between the two blocks.

    (* Start insertion in loop_bb. *)
    position_at_end loop_bb builder;

    (* Start the PHI node with an entry for start. *)
    let variable = build_phi [(start_val, preheader_bb)] var_name builder in

Now that the “preheader” for the loop is set up, we switch to emitting code for the loop body. To begin with, we move the insertion point and create the PHI node for the loop induction variable. Since we already know the incoming value for the starting value, we add it to the Phi node. Note that the Phi will eventually get a second value for the backedge, but we can’t set it up yet (because it doesn’t exist!).

    (* Within the loop, the variable is defined equal to the PHI node. If it
     * shadows an existing variable, we have to restore it, so save it
     * now. *)
    let old_val =
      try Some (Hashtbl.find named_values var_name) with Not_found -> None
    in
    Hashtbl.add named_values var_name variable;

    (* Emit the body of the loop.  This, like any other expr, can change the
     * current BB.  Note that we ignore the value computed by the body, but
     * don't allow an error *)
    ignore (codegen_expr body);

Now the code starts to get more interesting. Our ‘for’ loop introduces a new variable to the symbol table. This means that our symbol table can now contain either function arguments or loop variables. To handle this, before we codegen the body of the loop, we add the loop variable as the current value for its name. Note that it is possible that there is a variable of the same name in the outer scope. It would be easy to make this an error (emit an error and return null if there is already an entry for VarName) but we choose to allow shadowing of variables. In order to handle this correctly, we remember the Value that we are potentially shadowing in `old_val` (which will be None if there is no shadowed variable).

Once the loop variable is set into the symbol table, the code recursively codegen’s the body. This allows the body to use the loop variable: any references to it will naturally find it in the symbol table.

    (* Emit the step value. *)
    let step_val =
      match step with
      | Some step -> codegen_expr step
      (* If not specified, use 1.0. *)
      | None -> const_float double_type 1.0
    in

    let next_var = build_add variable step_val "nextvar" builder in

Now that the body is emitted, we compute the next value of the iteration variable by adding the step value, or 1.0 if it isn’t present. ‘`next_var`‘ will be the value of the loop variable on the next iteration of the loop.

    (* Compute the end condition. *)
    let end_cond = codegen_expr end_ in

    (* Convert condition to a bool by comparing equal to 0.0. *)
    let zero = const_float double_type 0.0 in
    let end_cond = build_fcmp Fcmp.One end_cond zero "loopcond" builder in

Finally, we evaluate the exit value of the loop, to determine whether the loop should exit. This mirrors the condition evaluation for the if/then/else statement.

    (* Create the "after loop" block and insert it. *)
    let loop_end_bb = insertion_block builder in
    let after_bb = append_block context "afterloop" the_function in

    (* Insert the conditional branch into the end of loop_end_bb. *)
    ignore (build_cond_br end_cond loop_bb after_bb builder);

    (* Any new code will be inserted in after_bb. *)
    position_at_end after_bb builder;

With the code for the body of the loop complete, we just need to finish up the control flow for it. This code remembers the end block (for the phi node), then creates the block for the loop exit (“afterloop”). Based on the value of the exit condition, it creates a conditional branch that chooses between executing the loop again and exiting the loop. Any future code is emitted in the “afterloop” block, so it sets the insertion position to it.

    (* Add a new entry to the PHI node for the backedge. *)
    add_incoming (next_var, loop_end_bb) variable;

    (* Restore the unshadowed variable. *)
    begin match old_val with
    | Some old_val -> Hashtbl.add named_values var_name old_val
    | None -> ()
    end;

    (* for expr always returns 0.0. *)
    const_null double_type

The final code handles various cleanups: now that we have the “`next_var`” value, we can add the incoming value to the loop PHI node. After that, we remove the loop variable from the symbol table, so that it isn’t in scope after the for loop. Finally, code generation of the for loop always returns 0.0, so that is what we return from `Codegen.codegen_expr`.

With this, we conclude the “adding control flow to Kaleidoscope” chapter of the tutorial. In this chapter we added two control flow constructs, and used them to motivate a couple of aspects of the LLVM IR that are important for front-end implementors to know. In the next chapter of our saga, we will get a bit crazier and add user-defined operators to our poor innocent language.

## 5.4. Full Code Listing

Here is the complete code listing for our running example, enhanced with the if/then/else and for expressions.. To build this example, use:

    # Compile
    ocamlbuild toy.byte
    # Run
    ./toy.byte

Here is the code:

_tags:

      <{lexer,parser}.ml>: use_camlp4, pp(camlp4of)
      <*.{byte,native}>: g++, use_llvm, use_llvm_analysis
      <*.{byte,native}>: use_llvm_executionengine, use_llvm_target
      <*.{byte,native}>: use_llvm_scalar_opts, use_bindings

myocamlbuild.ml:

      open Ocamlbuild_plugin;;

      ocaml_lib ~extern:true "llvm";;
      ocaml_lib ~extern:true "llvm_analysis";;
      ocaml_lib ~extern:true "llvm_executionengine";;
      ocaml_lib ~extern:true "llvm_target";;
      ocaml_lib ~extern:true "llvm_scalar_opts";;

      flag ["link"; "ocaml"; "g++"] (S[A"-cc"; A"g++"]);;
      dep ["link"; "ocaml"; "use_bindings"] ["bindings.o"];;

token.ml:

      (*===----------------------------------------------------------------------===
       * Lexer Tokens
       *===----------------------------------------------------------------------===*)

      (* The lexer returns these 'Kwd' if it is an unknown character, otherwise one of
       * these others for known things. *)
      type token =
        (* commands *)
        | Def | Extern

        (* primary *)
        | Ident of string | Number of float

        (* unknown *)
        | Kwd of char

        (* control *)
        | If | Then | Else
        | For | In

lexer.ml:

      (*===----------------------------------------------------------------------===
       * Lexer
       *===----------------------------------------------------------------------===*)

      let rec lex = parser
        (* Skip any whitespace. *)
        | [< ' (' ' | '\n' | '\r' | '\t'); stream >] -> lex stream

        (* identifier: [a-zA-Z][a-zA-Z0-9] *)
        | [< ' ('A' .. 'Z' | 'a' .. 'z' as c); stream >] ->
            let buffer = Buffer.create 1 in
            Buffer.add_char buffer c;
            lex_ident buffer stream

        (* number: [0-9.]+ *)
        | [< ' ('0' .. '9' as c); stream >] ->
            let buffer = Buffer.create 1 in
            Buffer.add_char buffer c;
            lex_number buffer stream

        (* Comment until end of line. *)
        | [< ' ('#'); stream >] ->
            lex_comment stream

        (* Otherwise, just return the character as its ascii value. *)
        | [< 'c; stream >] ->
            [< 'Token.Kwd c; lex stream >]

        (* end of stream. *)
        | [< >] -> [< >]

      and lex_number buffer = parser
        | [< ' ('0' .. '9' | '.' as c); stream >] ->
            Buffer.add_char buffer c;
            lex_number buffer stream
        | [< stream=lex >] ->
            [< 'Token.Number (float_of_string (Buffer.contents buffer)); stream >]

      and lex_ident buffer = parser
        | [< ' ('A' .. 'Z' | 'a' .. 'z' | '0' .. '9' as c); stream >] ->
            Buffer.add_char buffer c;
            lex_ident buffer stream
        | [< stream=lex >] ->
            match Buffer.contents buffer with
            | "def" -> [< 'Token.Def; stream >]
            | "extern" -> [< 'Token.Extern; stream >]
            | "if" -> [< 'Token.If; stream >]
            | "then" -> [< 'Token.Then; stream >]
            | "else" -> [< 'Token.Else; stream >]
            | "for" -> [< 'Token.For; stream >]
            | "in" -> [< 'Token.In; stream >]
            | id -> [< 'Token.Ident id; stream >]

      and lex_comment = parser
        | [< ' ('\n'); stream=lex >] -> stream
        | [< 'c; e=lex_comment >] -> e
        | [< >] -> [< >]

ast.ml:

      (*===----------------------------------------------------------------------===
       * Abstract Syntax Tree (aka Parse Tree)
       *===----------------------------------------------------------------------===*)

      (* expr - Base type for all expression nodes. *)
      type expr =
        (* variant for numeric literals like "1.0". *)
        | Number of float

        (* variant for referencing a variable, like "a". *)
        | Variable of string

        (* variant for a binary operator. *)
        | Binary of char * expr * expr

        (* variant for function calls. *)
        | Call of string * expr array

        (* variant for if/then/else. *)
        | If of expr * expr * expr

        (* variant for for/in. *)
        | For of string * expr * expr * expr option * expr

      (* proto - This type represents the "prototype" for a function, which captures
       * its name, and its argument names (thus implicitly the number of arguments the
       * function takes). *)
      type proto = Prototype of string * string array

      (* func - This type represents a function definition itself. *)
      type func = Function of proto * expr

parser.ml:

      (*===---------------------------------------------------------------------===
       * Parser
       *===---------------------------------------------------------------------===*)

      (* binop_precedence - This holds the precedence for each binary operator that is
       * defined *)
      let binop_precedence:(char, int) Hashtbl.t = Hashtbl.create 10

      (* precedence - Get the precedence of the pending binary operator token. *)
      let precedence c = try Hashtbl.find binop_precedence c with Not_found -> -1

      (* primary
       *   ::= identifier
       *   ::= numberexpr
       *   ::= parenexpr
       *   ::= ifexpr
       *   ::= forexpr *)
      let rec parse_primary = parser
        (* numberexpr ::= number *)
        | [< 'Token.Number n >] -> Ast.Number n

        (* parenexpr ::= '(' expression ')' *)
        | [< 'Token.Kwd '('; e=parse_expr; 'Token.Kwd ')' ?? "expected ')'" >] -> e

        (* identifierexpr
         *   ::= identifier
         *   ::= identifier '(' argumentexpr ')' *)
        | [< 'Token.Ident id; stream >] ->
            let rec parse_args accumulator = parser
              | [< e=parse_expr; stream >] ->
                  begin parser
                    | [< 'Token.Kwd ','; e=parse_args (e :: accumulator) >] -> e
                    | [< >] -> e :: accumulator
                  end stream
              | [< >] -> accumulator
            in
            let rec parse_ident id = parser
              (* Call. *)
              | [< 'Token.Kwd '(';
                   args=parse_args [];
                   'Token.Kwd ')' ?? "expected ')'">] ->
                  Ast.Call (id, Array.of_list (List.rev args))

              (* Simple variable ref. *)
              | [< >] -> Ast.Variable id
            in
            parse_ident id stream

        (* ifexpr ::= 'if' expr 'then' expr 'else' expr *)
        | [< 'Token.If; c=parse_expr;
             'Token.Then ?? "expected 'then'"; t=parse_expr;
             'Token.Else ?? "expected 'else'"; e=parse_expr >] ->
            Ast.If (c, t, e)

        (* forexpr
              ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression *)
        | [< 'Token.For;
             'Token.Ident id ?? "expected identifier after for";
             'Token.Kwd '=' ?? "expected '=' after for";
             stream >] ->
            begin parser
              | [<
                   start=parse_expr;
                   'Token.Kwd ',' ?? "expected ',' after for";
                   end_=parse_expr;
                   stream >] ->
                  let step =
                    begin parser
                    | [< 'Token.Kwd ','; step=parse_expr >] -> Some step
                    | [< >] -> None
                    end stream
                  in
                  begin parser
                  | [< 'Token.In; body=parse_expr >] ->
                      Ast.For (id, start, end_, step, body)
                  | [< >] ->
                      raise (Stream.Error "expected 'in' after for")
                  end stream
              | [< >] ->
                  raise (Stream.Error "expected '=' after for")
            end stream

        | [< >] -> raise (Stream.Error "unknown token when expecting an expression.")

      (* binoprhs
       *   ::= ('+' primary)* *)
      and parse_bin_rhs expr_prec lhs stream =
        match Stream.peek stream with
        (* If this is a binop, find its precedence. *)
        | Some (Token.Kwd c) when Hashtbl.mem binop_precedence c ->
            let token_prec = precedence c in

            (* If this is a binop that binds at least as tightly as the current binop,
             * consume it, otherwise we are done. *)
            if token_prec < expr_prec then lhs else begin
              (* Eat the binop. *)
              Stream.junk stream;

              (* Parse the primary expression after the binary operator. *)
              let rhs = parse_primary stream in

              (* Okay, we know this is a binop. *)
              let rhs =
                match Stream.peek stream with
                | Some (Token.Kwd c2) ->
                    (* If BinOp binds less tightly with rhs than the operator after
                     * rhs, let the pending operator take rhs as its lhs. *)
                    let next_prec = precedence c2 in
                    if token_prec < next_prec
                    then parse_bin_rhs (token_prec + 1) rhs stream
                    else rhs
                | _ -> rhs
              in

              (* Merge lhs/rhs. *)
              let lhs = Ast.Binary (c, lhs, rhs) in
              parse_bin_rhs expr_prec lhs stream
            end
        | _ -> lhs

      (* expression
       *   ::= primary binoprhs *)
      and parse_expr = parser
        | [< lhs=parse_primary; stream >] -> parse_bin_rhs 0 lhs stream

      (* prototype
       *   ::= id '(' id* ')' *)
      let parse_prototype =
        let rec parse_args accumulator = parser
          | [< 'Token.Ident id; e=parse_args (id::accumulator) >] -> e
          | [< >] -> accumulator
        in

        parser
        | [< 'Token.Ident id;
             'Token.Kwd '(' ?? "expected '(' in prototype";
             args=parse_args [];
             'Token.Kwd ')' ?? "expected ')' in prototype" >] ->
            (* success. *)
            Ast.Prototype (id, Array.of_list (List.rev args))

        | [< >] ->
            raise (Stream.Error "expected function name in prototype")

      (* definition ::= 'def' prototype expression *)
      let parse_definition = parser
        | [< 'Token.Def; p=parse_prototype; e=parse_expr >] ->
            Ast.Function (p, e)

      (* toplevelexpr ::= expression *)
      let parse_toplevel = parser
        | [< e=parse_expr >] ->
            (* Make an anonymous proto. *)
            Ast.Function (Ast.Prototype ("", [||]), e)

      (*  external ::= 'extern' prototype *)
      let parse_extern = parser
        | [< 'Token.Extern; e=parse_prototype >] -> e

codegen.ml:

      (*===----------------------------------------------------------------------===
       * Code Generation
       *===----------------------------------------------------------------------===*)

      open Llvm

      exception Error of string

      let context = global_context ()
      let the_module = create_module context "my cool jit"
      let builder = builder context
      let named_values:(string, llvalue) Hashtbl.t = Hashtbl.create 10
      let double_type = double_type context

      let rec codegen_expr = function
        | Ast.Number n -> const_float double_type n
        | Ast.Variable name ->
            (try Hashtbl.find named_values name with
              | Not_found -> raise (Error "unknown variable name"))
        | Ast.Binary (op, lhs, rhs) ->
            let lhs_val = codegen_expr lhs in
            let rhs_val = codegen_expr rhs in
            begin
              match op with
              | '+' -> build_add lhs_val rhs_val "addtmp" builder
              | '-' -> build_sub lhs_val rhs_val "subtmp" builder
              | '*' -> build_mul lhs_val rhs_val "multmp" builder
              | '<' ->
                  (* Convert bool 0/1 to double 0.0 or 1.0 *)
                  let i = build_fcmp Fcmp.Ult lhs_val rhs_val "cmptmp" builder in
                  build_uitofp i double_type "booltmp" builder
              | _ -> raise (Error "invalid binary operator")
            end
        | Ast.Call (callee, args) ->
            (* Look up the name in the module table. *)
            let callee =
              match lookup_function callee the_module with
              | Some callee -> callee
              | None -> raise (Error "unknown function referenced")
            in
            let params = params callee in

            (* If argument mismatch error. *)
            if Array.length params == Array.length args then () else
              raise (Error "incorrect # arguments passed");
            let args = Array.map codegen_expr args in
            build_call callee args "calltmp" builder
        | Ast.If (cond, then_, else_) ->
            let cond = codegen_expr cond in

            (* Convert condition to a bool by comparing equal to 0.0 *)
            let zero = const_float double_type 0.0 in
            let cond_val = build_fcmp Fcmp.One cond zero "ifcond" builder in

            (* Grab the first block so that we might later add the conditional branch
             * to it at the end of the function. *)
            let start_bb = insertion_block builder in
            let the_function = block_parent start_bb in

            let then_bb = append_block context "then" the_function in

            (* Emit 'then' value. *)
            position_at_end then_bb builder;
            let then_val = codegen_expr then_ in

            (* Codegen of 'then' can change the current block, update then_bb for the
             * phi. We create a new name because one is used for the phi node, and the
             * other is used for the conditional branch. *)
            let new_then_bb = insertion_block builder in

            (* Emit 'else' value. *)
            let else_bb = append_block context "else" the_function in
            position_at_end else_bb builder;
            let else_val = codegen_expr else_ in

            (* Codegen of 'else' can change the current block, update else_bb for the
             * phi. *)
            let new_else_bb = insertion_block builder in

            (* Emit merge block. *)
            let merge_bb = append_block context "ifcont" the_function in
            position_at_end merge_bb builder;
            let incoming = [(then_val, new_then_bb); (else_val, new_else_bb)] in
            let phi = build_phi incoming "iftmp" builder in

            (* Return to the start block to add the conditional branch. *)
            position_at_end start_bb builder;
            ignore (build_cond_br cond_val then_bb else_bb builder);

            (* Set a unconditional branch at the end of the 'then' block and the
             * 'else' block to the 'merge' block. *)
            position_at_end new_then_bb builder; ignore (build_br merge_bb builder);
            position_at_end new_else_bb builder; ignore (build_br merge_bb builder);

            (* Finally, set the builder to the end of the merge block. *)
            position_at_end merge_bb builder;

            phi
        | Ast.For (var_name, start, end_, step, body) ->
            (* Emit the start code first, without 'variable' in scope. *)
            let start_val = codegen_expr start in

            (* Make the new basic block for the loop header, inserting after current
             * block. *)
            let preheader_bb = insertion_block builder in
            let the_function = block_parent preheader_bb in
            let loop_bb = append_block context "loop" the_function in

            (* Insert an explicit fall through from the current block to the
             * loop_bb. *)
            ignore (build_br loop_bb builder);

            (* Start insertion in loop_bb. *)
            position_at_end loop_bb builder;

            (* Start the PHI node with an entry for start. *)
            let variable = build_phi [(start_val, preheader_bb)] var_name builder in

            (* Within the loop, the variable is defined equal to the PHI node. If it
             * shadows an existing variable, we have to restore it, so save it
             * now. *)
            let old_val =
              try Some (Hashtbl.find named_values var_name) with Not_found -> None
            in
            Hashtbl.add named_values var_name variable;

            (* Emit the body of the loop.  This, like any other expr, can change the
             * current BB.  Note that we ignore the value computed by the body, but
             * don't allow an error *)
            ignore (codegen_expr body);

            (* Emit the step value. *)
            let step_val =
              match step with
              | Some step -> codegen_expr step
              (* If not specified, use 1.0. *)
              | None -> const_float double_type 1.0
            in

            let next_var = build_add variable step_val "nextvar" builder in

            (* Compute the end condition. *)
            let end_cond = codegen_expr end_ in

            (* Convert condition to a bool by comparing equal to 0.0. *)
            let zero = const_float double_type 0.0 in
            let end_cond = build_fcmp Fcmp.One end_cond zero "loopcond" builder in

            (* Create the "after loop" block and insert it. *)
            let loop_end_bb = insertion_block builder in
            let after_bb = append_block context "afterloop" the_function in

            (* Insert the conditional branch into the end of loop_end_bb. *)
            ignore (build_cond_br end_cond loop_bb after_bb builder);

            (* Any new code will be inserted in after_bb. *)
            position_at_end after_bb builder;

            (* Add a new entry to the PHI node for the backedge. *)
            add_incoming (next_var, loop_end_bb) variable;

            (* Restore the unshadowed variable. *)
            begin match old_val with
            | Some old_val -> Hashtbl.add named_values var_name old_val
            | None -> ()
            end;

            (* for expr always returns 0.0. *)
            const_null double_type

      let codegen_proto = function
        | Ast.Prototype (name, args) ->
            (* Make the function type: double(double,double) etc. *)
            let doubles = Array.make (Array.length args) double_type in
            let ft = function_type double_type doubles in
            let f =
              match lookup_function name the_module with
              | None -> declare_function name ft the_module

              (* If 'f' conflicted, there was already something named 'name'. If it
               * has a body, don't allow redefinition or reextern. *)
              | Some f ->
                  (* If 'f' already has a body, reject this. *)
                  if block_begin f <> At_end f then
                    raise (Error "redefinition of function");

                  (* If 'f' took a different number of arguments, reject. *)
                  if element_type (type_of f) <> ft then
                    raise (Error "redefinition of function with different # args");
                  f
            in

            (* Set names for all arguments. *)
            Array.iteri (fun i a ->
              let n = args.(i) in
              set_value_name n a;
              Hashtbl.add named_values n a;
            ) (params f);
            f

      let codegen_func the_fpm = function
        | Ast.Function (proto, body) ->
            Hashtbl.clear named_values;
            let the_function = codegen_proto proto in

            (* Create a new basic block to start insertion into. *)
            let bb = append_block context "entry" the_function in
            position_at_end bb builder;

            try
              let ret_val = codegen_expr body in

              (* Finish off the function. *)
              let _ = build_ret ret_val builder in

              (* Validate the generated code, checking for consistency. *)
              Llvm_analysis.assert_valid_function the_function;

              (* Optimize the function. *)
              let _ = PassManager.run_function the_function the_fpm in

              the_function
            with e ->
              delete_function the_function;
              raise e

toplevel.ml:

      (*===----------------------------------------------------------------------===
       * Top-Level parsing and JIT Driver
       *===----------------------------------------------------------------------===*)

      open Llvm
      open Llvm_executionengine

      (* top ::= definition | external | expression | ';' *)
      let rec main_loop the_fpm the_execution_engine stream =
        match Stream.peek stream with
        | None -> ()

        (* ignore top-level semicolons. *)
        | Some (Token.Kwd ';') ->
            Stream.junk stream;
            main_loop the_fpm the_execution_engine stream

        | Some token ->
            begin
              try match token with
              | Token.Def ->
                  let e = Parser.parse_definition stream in
                  print_endline "parsed a function definition.";
                  dump_value (Codegen.codegen_func the_fpm e);
              | Token.Extern ->
                  let e = Parser.parse_extern stream in
                  print_endline "parsed an extern.";
                  dump_value (Codegen.codegen_proto e);
              | _ ->
                  (* Evaluate a top-level expression into an anonymous function. *)
                  let e = Parser.parse_toplevel stream in
                  print_endline "parsed a top-level expr";
                  let the_function = Codegen.codegen_func the_fpm e in
                  dump_value the_function;

                  (* JIT the function, returning a function pointer. *)
                  let result = ExecutionEngine.run_function the_function [||]
                    the_execution_engine in

                  print_string "Evaluated to ";
                  print_float (GenericValue.as_float Codegen.double_type result);
                  print_newline ();
              with Stream.Error s | Codegen.Error s ->
                (* Skip token for error recovery. *)
                Stream.junk stream;
                print_endline s;
            end;
            print_string "ready> "; flush stdout;
            main_loop the_fpm the_execution_engine stream

toy.ml:

      (*===----------------------------------------------------------------------===
       * Main driver code.
       *===----------------------------------------------------------------------===*)

      open Llvm
      open Llvm_executionengine
      open Llvm_target
      open Llvm_scalar_opts

      let main () =
        ignore (initialize_native_target ());

        (* Install standard binary operators.
         * 1 is the lowest precedence. *)
        Hashtbl.add Parser.binop_precedence '<' 10;
        Hashtbl.add Parser.binop_precedence '+' 20;
        Hashtbl.add Parser.binop_precedence '-' 20;
        Hashtbl.add Parser.binop_precedence '*' 40;    (* highest. *)

        (* Prime the first token. *)
        print_string "ready> "; flush stdout;
        let stream = Lexer.lex (Stream.of_channel stdin) in

        (* Create the JIT. *)
        let the_execution_engine = ExecutionEngine.create Codegen.the_module in
        let the_fpm = PassManager.create_function Codegen.the_module in

        (* Set up the optimizer pipeline.  Start with registering info about how the
         * target lays out data structures. *)
        DataLayout.add (ExecutionEngine.target_data the_execution_engine) the_fpm;

        (* Do simple "peephole" optimizations and bit-twiddling optzn. *)
        add_instruction_combination the_fpm;

        (* reassociate expressions. *)
        add_reassociation the_fpm;

        (* Eliminate Common SubExpressions. *)
        add_gvn the_fpm;

        (* Simplify the control flow graph (deleting unreachable blocks, etc). *)
        add_cfg_simplification the_fpm;

        ignore (PassManager.initialize the_fpm);

        (* Run the main "interpreter loop" now. *)
        Toplevel.main_loop the_fpm the_execution_engine stream;

        (* Print out all the generated code. *)
        dump_module Codegen.the_module
      ;;

      main ()

bindings.c

      #include <stdio.h>

      /* putchard - putchar that takes a double and returns 0. */
      extern double putchard(double X) {
        putchar((char)X);
        return 0;
      }

Next: Extending the language: user-defined operators